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#### Introduction To Probability Theory Important Questions

11th Standard

Reg.No. :
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Maths

Time : 01:40:00 Hrs
Total Marks : 50

Part A

10 x 1 = 10
1. A, B, and C try to hit a target simultaneously but independently. Their respective probabilities of hitting the target are${3\over4},{1\over2},{5\over 8}$. The probability that the target is hit by A or B but not by C is

(a)

${21\over64}$

(b)

${7\over32}$

(c)

${9\over64}$

(d)

${7\over8}$

2. A bag contains 5 white and 3 black balls. Five balls are drawn successively without replacement. The probability that they are alternately of different colours is

(a)

${3\over 14}$

(b)

${5\over 14}$

(c)

${1\over 14}$

(d)

${9\over 14}$

3. If two events A and B are independent such that P(A)=0.35 and $P(A\cup B)=0.6$ ,then P(B) is

(a)

${5\over 13}$

(b)

${1\over 13}$

(c)

${4\over 13}$

(d)

${7\over 13}$

4. If m is a number such that m $\le$ 5, then the probability that quadratic equation 2x2+2mx+m+1=0 has real roots is

(a)

${1\over 5}$

(b)

${2\over 5}$

(c)

${3\over 5}$

(d)

${4\over 5}$

5. A speaks truth in 75% cases and B speaks truth in 80% cases. Probability that they contradict each other in a statement is

(a)

$\frac { 7 }{ 20 }$

(b)

$\frac { 13 }{ 20 }$

(c)

$\frac { 3 }{ 5 }$

(d)

$\frac { 2 }{ 5 }$

6. A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect is

(a)

$\frac { 64 }{ 64 }$

(b)

$\frac { 49 }{ 64 }$

(c)

$\frac { 40 }{ 64 }$

(d)

$\frac { 24 }{ 64 }$

7. If A and B are two events such that P(A) = $\frac { 4 }{ 5 }$ and $P(A\cap B)=\frac { 7 }{ 10 }$ then P(B/A) =

(a)

$\frac { 1 }{ 10 }$

(b)

$\frac { 1 }{ 8 }$

(c)

$\frac { 7 }{ 8 }$

(d)

$\frac { 17 }{ 20 }$

8. If P(A)=$\frac { 1 }{ 2 }$, P(B)=$\frac { 1 }{ 3 }$ and P(A/B) = $\frac { 1 }{ 4 }$, then $P(\bar { A } \cap \bar { B } )$ =

(a)

$\frac { 1 }{ 12 }$

(b)

$\frac { 3 }{ 4 }$

(c)

$\frac { 1 }{ 4 }$

(d)

$\frac { 3 }{ 16 }$

9. If P(A) = 0.4, P(B) = 0.3 and P(AUB) = 0.5, then $P(\bar { B } \cap A)$

(a)

$\frac { 2 }{ 3 }$

(b)

$\frac { 1 }{ 2 }$

(c)

$\frac { 3 }{ 10 }$

(d)

$\frac { 1 }{ 5 }$

10. A flash light has 8 batteries out of which 3 are dead. If 2 batteries are selected without replacement and tested, the probability that both are dead is

(a)

$\frac { 3 }{ 28 }$

(b)

$\frac { 1 }{ 14 }$

(c)

$\frac { 9 }{ 64 }$

(d)

$\frac { 33 }{ 56 }$

11. Part B

5 x 2 = 10
12. If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible
$P(A)=\frac { 1 }{ \sqrt { 3 } } ,\quad P(B)-1-\frac { 1 }{ \sqrt { 3 } } ,\quad P(C)-0$

13. An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible
P(A) = 0.22 , P(B) = 0.38 , P(C) = 0. 16, P (D) = 0.34

14. Given that P(A) =0.52, P(B)=0.43, and P(A∩B)=0.24, find
P(A∪B)

15. The probability that student selected at random from a class will pass in Mathematics is $\frac { 2 }{ 3 }$ and the probability that he passes in Mathematics and English is $\frac { 1 }{ 3 }$. What is the probability that he will pass in English if it is known that he has passed in Mathematics?

16. Given that the events A and B are such that P(A) = $\frac { 1 }{ 2 }$, P(AUB) = $\frac { 3 }{ 5 }$ and P(B) = p. find P if they are mutually exclusive events.

17. Part C

5 x 3 = 15
18. A problem in Mathematics is given to three students whose chances of solving A problem in Mathematics is given to three students whose chances of solving $\frac { 1 }{ 3 } ,\frac { 1 }{ 4 }$ and $\frac { 1 }{ 5 }$ (i) What is the probability that the problem is solved? (ii) What is the probability that exactly one of them will solve it?

19. A firm manufactures PVC pipes in three plants viz, X, Y, and Z. The daily production volumes from the three firms X, Y and Z are respectively 2000 units, 3000 units, and 5000 units. It is known from the past experience that 3% of the output from plant X, 4% from plant Y and 2% from plant Z are defective. A pipe is selected at random from a day’s total production,
(i) find the probability that the selected pipe is a defective one.
(ii) if the selected pipe is a defective, then what is the probability that it was produced by plant Y?

20. The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of
(i) $P(A\cup B)$
(ii) $P(A\cap \bar { B } )$
(iii) $P(\bar { A } \cap B)$

21. One card is drawn from a well shuffled pack of 52 cards. If E is the event, "the card drawn is a king or queen" and F is the event "the card drawn is a queen or an ace", then find P(E/F).

22. A bag contains 10 white and 15 black balls. 2 balls are drawn in succession without replacement. What is the probability that first is white and second is black?

23. Part D

3 x 5 = 15
24. If A and B are two independent events such that P(A$\cup$B)=0.6, P(A)=0.2,  find P(B).

25. Two cards are drawn from a pack of 52 cards in succession. Find the probability that both are Jack when the first drawn card is (i) replaced (ii) not replaced.

26. Urn-I contains 8 red and 4 blue balls and urn-II contains 5 red and 10 blue balls. One urn is chosen at random and two balls are drawn from it. Find the probability that both balls are red.